Solve for $x$ and $y$ using elimination. ${-3x-3y = -48}$ ${-4x+3y = 6}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-7x = -42$ $\dfrac{-7x}{{-7}} = \dfrac{-42}{{-7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x-3y = -48}\thinspace$ to find $y$ ${-3}{(6)}{ - 3y = -48}$ $-18-3y = -48$ $-18{+18} - 3y = -48{+18}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {-4x+3y = 6}\thinspace$ and get the same answer for $y$ : ${-4}{(6)}{ + 3y = 6}$ ${y = 10}$